Detection of time reversibility in time series by ordinal patterns analysis

Time irreversibility is a common signature of nonlinear processes, and a fundamental property of non-equilibrium systems driven by non-conservative forces. A time series is said to be reversible if its statistical properties are invariant regardless of the direction of time. Here we propose the Time Reversibility from Ordinal Patterns method (TiROP) to assess time-reversibility from an observed finite time series. TiROP captures the information of scalar observations in time forward, as well as its time-reversed counterpart by means of ordinal patterns. The method compares both underlying information contents by quantifying its (dis)-similarity via Jensen-Shannon divergence. The statistic is contrasted with a population of divergences coming from a set of surrogates to unveil the temporal nature and its involved time scales. We tested TiROP in different synthetic and real, linear and non linear time series, juxtaposed with results from the classical Ramsey's time reversibility test. Our results depict a novel, fast-computation, and fully data-driven methodology to assess time-reversibility at different time scales with no further assumptions over data. This approach adds new insights about the current non-linear analysis techniques, and also could shed light on determining new physiological biomarkers of high reliability and computational efficiency.Comment: 8 pages, 5 figures, 1 tabl

History of art paintings through the lens of entropy and complexity

Art is the ultimate expression of human creativity that is deeply influenced by the philosophy and culture of the corresponding historical epoch. The quantitative analysis of art is therefore essential for better understanding human cultural evolution. Here we present a large-scale quantitative analysis of almost 140 thousand paintings, spanning nearly a millennium of art history. Based on the local spatial patterns in the images of these paintings, we estimate the permutation entropy and the statistical complexity of each painting. These measures map the degree of visual order of artworks into a scale of order-disorder and simplicity-complexity that locally reflects qualitative categories proposed by art historians. The dynamical behavior of these measures reveals a clear temporal evolution of art, marked by transitions that agree with the main historical periods of art. Our research shows that different artistic styles have a distinct average degree of entropy and complexity, thus allowing a hierarchical organization and clustering of styles according to these metrics. We have further verified that the identified groups correspond well with the textual content used to qualitatively describe the styles, and that the employed complexity-entropy measures can be used for an effective classification of artworks.Comment: 10 two-column pages, 5 figures; accepted for publication in PNAS [supplementary information available at http://www.pnas.org/highwire/filestream/824089/field_highwire_adjunct_files/0/pnas.1800083115.sapp.pdf

노래 신호의 자동 전사

학위논문 (박사)-- 서울대학교 융합과학기술대학원 융합과학부, 2017. 8. 이교구.Automatic music transcription refers to an automatic extraction of musical attributes such as notes from an audio signal to a symbolic level. The symbolized music data are applicable for various purposes such as music education and production by providing higher-level information to both consumers and creators. Although the singing voice is the easiest one to listen and play among various music signals, traditional transcription methods for musical instruments are not suitable due to the acoustic complexity in the human voice. The main goal of this thesis is to develop a fully-automatic singing transcription system that exceeds existing methods. We first take a look at some typical approaches for pitch tracking and onset detection, which are two fundamental tasks of music transcription, and then propose several methods for each task. In terms of pitch tracking, we examine the effect of data sampling on the performance of periodicity analysis of music signals. For onset detection, the local homogeneity in the harmonic structure is exploited through the cepstral analysis and unsupervised classification. The final transcription system includes feature extraction and probabilistic model of the harmonic structure, and note transition based on the hidden Markov model. It achieved the best performance (an F-measure of 82%) in the note-level evaluation including the state-of-the-art systems.Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Definitions 5 1.2.1 Musical keywords 5 1.2.2 Scientific keywords 7 1.2.3 Representations 7 1.3 Problems in singing transcription 9 1.4 Topics of interest 10 1.5 Outline of the thesis 13 Chapter 2 Background 16 2.1 Pitch estimation 17 2.1.1 Time-domain methods 17 2.1.2 Frequency-domain methods 18 2.2 Note segmentation 20 2.2.1 Onset detection 20 2.2.2 Offset detection 23 2.3 Singing transcription 24 2.4 Evaluation methodology 26 2.4.1 Pitch estimation 26 2.4.2 Note segmentation 27 2.4.3 Dataset 28 2.5 Summary 31 Chapter 3 Periodicity Analysis by Sampling in the Time/Frequency Domain for Pitch Tracking 32 3.1 Introduction 32 3.2 Data sampling 34 3.3 Sampled ACF/DF in the time domain 37 3.4 Sampled ACF/DF in the frequency domain 38 3.5 Iterative F0 estimation 40 3.6 Experimental setup 42 3.7 Result 46 3.8 Summary 49 Chapter 4 Note Onset Detection based on Harmonic Cepstrum regularity 50 4.1 Introduction 50 4.2 Cepstral analysis 52 4.3 Harmonic cepstrum regularity 56 4.3.1 Harmonic quefrency selection 57 4.3.2 Sub-harmonic regularity function 58 4.3.3 Adaptive thresholding 59 4.3.4 Picking onsets 59 4.4 Experiments 61 4.4.1 Dataset description 61 4.4.2 Evaluation results 62 4.5 Summary 64 Chapter 5 Robust Singing Transcription System using Local Homogeneity in the Harmonic Structure 66 5.1 Introduction 66 5.2 F0 tracking 71 5.3 Feature extraction 72 5.4 Mixture model 76 5.5 Note detection 80 5.5.1 Transition boundary detection 81 5.5.2 Note boundary selection 83 5.5.3 Note pitch decision 84 5.6 Evaluation 86 5.6.1 Dataset 86 5.6.2 Criteria and measures 87 5.6.3 Experimental setup 89 5.7 Results and discussions 90 5.7.1 Failure analysis 95 5.8 Summary 97 Chapter 6 Conclusion and Future Work 99 6.1 Contributions 99 6.2 Future work 103 6.2.1 Precise partial tracking using instantaneous frequency 103 6.2.2 Linguistic model for note segmentation 105 Appendix 108 Derivation of the instantaneous frequency 108 Bibliography 110 초 록 124Docto

Invariance of visual operations at the level of receptive fields

Receptive field profiles registered by cell recordings have shown that mammalian vision has developed receptive fields tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time. This article presents a theoretical model by which families of idealized receptive field profiles can be derived mathematically from a small set of basic assumptions that correspond to structural properties of the environment. The article also presents a theory for how basic invariance properties to variations in scale, viewing direction and relative motion can be obtained from the output of such receptive fields, using complementary selection mechanisms that operate over the output of families of receptive fields tuned to different parameters. Thereby, the theory shows how basic invariance properties of a visual system can be obtained already at the level of receptive fields, and we can explain the different shapes of receptive field profiles found in biological vision from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.Comment: 40 pages, 17 figure